Colloquium: Atomic quantum gases in periodically driven optical lattices

Dynamics of quantum many-body systems is one of the most complex problems in physics since it involves the time evolution of a large number of particles that interact with each other under the influence of external forces. With ultracold atoms in optical atomic lattices it can be done in a controlled environment by applying a periodic force. This Colloquium covers the experimental and theoretical developments in this exciting field of physics.